Earth's dynamo limit of predictability controlled by magnetic dissipation

To constrain the forecast horizon of geomagnetic data assimilation, it is of interest to quantify the range of predictability of the geodynamo. Following earlier work in the field of dynamic meteorology, we investigate the sensitivity of numerical dynamos to various perturbations applied to the magnetic, velocity and temperature fields. These perturbations result in some errors, which affect all fields in the same relative way, and grow at the same exponential rate lambda = tau(-1)(e), independent of the type and the amplitude of perturbation. Errors produced by the limited resolution of numerical dynamos are also shown to produce a similar amplification, with the same exponential rate. Exploring various possible scaling laws, we demonstrate that the growth rate is mainly proportional to an advection timescale. To better understand the mechanism responsible for the error amplification, we next compare these growth rates with two other dynamo outputs which display a similar dependence on advection: the inverse tau(-1)(SV) of the secular-variation timescale, characterizing the secular variation of the observable field produced by these dynamos; and the inverse (tau(mag)(diss))(-1) of the magnetic dissipation time, characterizing the rate at which magnetic energy is produced to compensate for Ohmic dissipation in these dynamos. The possible role of viscous dissipation is also discussed via the inverse (t(diss)(kin))(-1) of the analogous viscous dissipation time, characterizing the rate at which kinetic energy is produced to compensate for viscous dissipation. We conclude that tau(e) tends to equate tau(mag)(diss) for dynamos operating in a turbulent regime with low enough Ekman number, and such that tau(mag)(diss) < tau(kin)(diss). As these conditions are met in the Earth's outer core, we suggest that tau(e) is controlled by magnetic dissipation, leading to a value tau(e) = tau(mag)(diss) approximate to 30 yr. We finally discuss the consequences of our results for the practical limit of predictability of the geodynamo.